A Fatou Type Theorem for a Special Non-symmetric Tube Domain
Author :
Publisher :
Page : 60 pages
File Size : 30,91 MB
Release : 1969
Category : Dissertations, Academic
ISBN :
Author :
Publisher :
Page : 60 pages
File Size : 30,91 MB
Release : 1969
Category : Dissertations, Academic
ISBN :
Author : F. Di Biase
Publisher : Springer Science & Business Media
Page : 158 pages
File Size : 25,28 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461223105
A basic principle governing the boundary behaviour of holomorphic func tions (and harmonic functions) is this: Under certain growth conditions, for almost every point in the boundary of the domain, these functions ad mit a boundary limit, if we approach the bounda-ry point within certain approach regions. For example, for bounded harmonic functions in the open unit disc, the natural approach regions are nontangential triangles with one vertex in the boundary point, and entirely contained in the disc [Fat06]. In fact, these natural approach regions are optimal, in the sense that convergence will fail if we approach the boundary inside larger regions, having a higher order of contact with the boundary. The first theorem of this sort is due to J. E. Littlewood [Lit27], who proved that if we replace a nontangential region with the rotates of any fixed tangential curve, then convergence fails. In 1984, A. Nagel and E. M. Stein proved that in Euclidean half spaces (and the unit disc) there are in effect regions of convergence that are not nontangential: These larger approach regions contain tangential sequences (as opposed to tangential curves). The phenomenon discovered by Nagel and Stein indicates that the boundary behaviour of ho)omor phic functions (and harmonic functions), in theorems of Fatou type, is regulated by a second principle, which predicts the existence of regions of convergence that are sequentially larger than the natural ones.
Author : American Mathematical Society
Publisher :
Page : 1356 pages
File Size : 44,53 MB
Release : 1969
Category : Mathematics
ISBN :
Author : Library of Congress. Copyright Office
Publisher : Copyright Office, Library of Congress
Page : 1830 pages
File Size : 32,48 MB
Release : 1972
Category : Copyright
ISBN :
Author : Library of Congress. Copyright Office
Publisher :
Page : 822 pages
File Size : 40,56 MB
Release : 1972
Category : American literature
ISBN :
Author : Library of Congress. Copyright Office
Publisher :
Page : 1540 pages
File Size : 26,66 MB
Release : 1970
Category : Copyright
ISBN :
The record of each copyright registration listed in the Catalog includes a description of the work copyrighted and data relating to the copyright claim (the name of the copyright claimant as given in the application for registration, the copyright date, the copyright registration number, etc.).
Author : Fausto Di Biase
Publisher :
Page : 152 pages
File Size : 32,83 MB
Release : 1997
Category : Fatou theorems
ISBN :
Author :
Publisher :
Page : 500 pages
File Size : 44,44 MB
Release : 1971
Category : Dissertation abstracts
ISBN :
Author : Phillip Griffiths
Publisher : American Mathematical Soc.
Page : 657 pages
File Size : 48,4 MB
Release : 1989
Category : Education
ISBN : 0821845306
"This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations - that is, representations on solution spaces of invariant differential equations."--BOOK JACKET.
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 13,11 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9401512795
This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.